Question

Find the equation to the sphere through o=(0,0,0)and making intercepts a,b,c on the axes

Answer 1

The equation to the sphere through (0,0,0) and making intercepts a,b,c on the axes is x² + y² + z² - ax - by - cz = 0

Step-by-step explanation:

Since the intercepts on x, y and z axes are a, b, c respectively

Therefore,

The points of intersection of the sphere on x, y, z axis will be respectively

$(a, 0, 0), (0,b,0), (0,0,c)$

The sphere also passes through (0, 0, 0)

Let the equation of the sphere be

$x^2+y^2+z^2+2ux+2vy+2wz+d=0$

Since the sphere passes through O  (0, 0, 0)

Therefore,

$0^2+0^2+0^2+2u\times 0+2v\times 0+2w\times 0+d=0$

$\implies d=0$

Similarly,

Since the sphere passes through (a, 0, 0)

Therefore,

$a^2+0+0+2ua+0+0+0=0$

$\implies a^2+2ua=0$

$\implies a(a+2u)=0$

But $a\ne 0$

$\implies u=-\frac{a}{2}$

Similarly we can find out that

$v=-\frac{b}{2}$

And $w=-\frac{c}{2}$

Therefore, the equation of the sphere will be

$x^2+y^2+z^2-ax-by-cz=0$

Hope this answer is helpful.

Know More:

Q: Equation of circle through 3 points (a,0,0), (0,b,0) and (0,0,c)?

Click Here: https://brainly.in/question/8527799

Q: Find the equation of the sphere with centre (1, -1, 2) and radius 3​?

Click Here: https://brainly.in/question/13635218